Disclaimer of Bias
My bias, to be clear, is in favor of rejecting ID, but I do acknowledge that there's prima facie grounds for accepting the argument that ID is a scientific theory. ID, however, relies on certain metaphysical presumptions that fall apart under scrutiny, and when properly met, falls outside of contemporary demarcation of science (though to be accurate, if you use a 19th century definition of science, ID works just fine). You're not looking for why philosophers of science reject ID as pseudoscience, so let's answer your question instead.
Intelligent Design, Infinite Regress, and Aliens
Intelligent design naturally leads to the question, if a naturalistic and evolutionary approach to the explanation to the existence of biological organisms is insufficient to explain the existence of said organisms, where does the intelligent designer come from? So you are right in that it mimics the form of the question of the first cause. Technically, there's nothing inherently wrong metaphysically accepting infinite regress when isolated from broader questions of cosmogony. Why can't there be an infinite cycle of IDers? I don't see on the face why there can't if the question is taken without considering the position of a naturalistic universe itself. In this way, one only metaphysically rejects an infinite cycle of IDers, if one considers the broader program of materialism and naturalism in describing the universe.
But even if one accepts ID as scientific, since there's nothing philosophically objectionable about an intelligent designer on the face, and ID certainly doesn't necessarily imply creationism. One could read it as a theory that advocates that space aliens seeded our DNA (Forbes) instead. So, it's possible to argue the universe has always existed with intelligence, and that one intelligent species designs the next, ad infinitum. In my mind it begs questions, but certainly it's not an irrational first principle if one accepts the universe has this infinite property. This is actually a foundationalist argument insofar as, there is a first principle, and it sits nicely along the principle of sufficient reason. One can even kick the question of the origin of the universe down the road with quantum physical speculation about a multiverse. Our universe was caused by another universe.
Now, you're asking if this metaphysical speculation inherently disqualifies ID, and from a rational standpoint, no, it doesn't. There is no logical contradiction that forces us to eliminate infinite regress as a metaphysical necessity (SEP), and anyone who says so isn't familiar with the Agrippan arguments or deeper epistemological conversation about foundationalism, infinite regress, and circularity.
Where the Metaphysical Problem with Infinite Design Actually Lies
ID has a Medieval conception of biological category and suffers from category mistakes. That is, it presumes natural kinds (SEP) which has two ideas that are opposed by modern empirical findings. If might be understood defending:
- There is a privileged notion of an organism, such as the chicken, which exists independently of interpretation.
- It conflates chicken-as-species with chicken-as-organism, a violation of the type-token distinction.
Let's say I design a classic Roman arch to be be built of bricks with the last piece to be placed the keystone. Certainly, if I come across an arch, I can say, it's not possible for a keystone to have come to this position naturally, for if I remove it, the arch will collapse, the two sides falling apart. Thus, with arches there is "irreducible complexity" because there are no natural steps that lead to a keystone existing in such a state in nature without a designer. One can then point to a natural arch and argue see, and if I pull the section out were the keystone would be in an arch, it too falls apart, so there must be a designer just like our Roman arch was designed. There is no step in construction that prevents the top portion of the arch to get in place naturally.
The error in this analogy to the reasoning of ID is obvious. Natural arches aren't constructed and they have no keystones. This is a serious category error, and all the meaning distraction of "complexity" is a smokescreen that hides the flaw. The flaw in the reasoning has to do with categories, not infinite regression. How so?
The chicken begets the egg begets the chicken...
Infinite regress right? How can there be chickens or eggs without a supreme being creating the infinite regress in the first place? See, the infinite regress isn't logically problematic. Chickens do beget chicken eggs. And chicken eggs do lead to chickens. There's nothing irrational about that regress. It makes sense. The problem is with the categories. Simply put, a chicken-as-organism is an instance of a chicken-as-species, and so to reason about the origin of chicken-as-organism presuming that it's not a graded member of a fuzzy category chicken-as-species is the category mistake. Ultimately, by seeing that the definition of chicken-as-organism is interrelated with the genetic and statistical membership to the chicken-as-species, and that the definition of chicken-as-species arises from dinosaur-as-species to bird-as-species through evolution of dinosaurs-as-organisms towards birds-as organisms. The problem dissolves.
This is a fallacy of composition where properties of the systems (instances of times such that we consider an organism at time x) are different from the system as a whole (all instances when considering organisms and collections of organisms). To point to the heart, and say, there's no step this chicken can exist without a heart, presumes both the category of the chicken and category of the heart, and PRESUME those categories aren't fuzzy and malleable. But they are.
What is a chicken and what is a heart may be fixed in this point or range in time, but not over the entire spectrum of time. Circulatory systems start off WITHOUT hearts and gradually evolve to have them, just as dinosaurs slowly change into birds WITHOUT a privileged point in time where chickens spring into being.
Thus, the belief in natural kinds displays an ignorance of categories in the same way that intelligent design does. The problem with intelligent design is not the infinite regress, it's the category mistake it presupposes by having a static and crisp hierarchy of categories instead of presuming a continuous and fuzzy evolution of categories. That's why today in biology, cladistics is the authoritative system for understanding our the taxonomy of living beings.
From a metaphysical standpoint, there's nothing wrong with intelligent design logically prima facie if one doesn't understand fuzzy categories and presumes natural kinds, but modern philosophers have shown that such presumptions are less than adequate for contemporary scientific enterprise which overstate objective reality. 'Chickens' and 'hearts' may have objective constituency in terms of matter, but the explanatory criteria to determine their membership is conventional and utilitarian.
To show how our categories are constructs of the mind, not independently existing facts about the universe, consider how a planet like Pluto is demoted to a TNO. People who understand the nature of categories (they're nominalistic (SEP) conventions), don't object. People who struggle with more rational, less intuitive notions of categorization reject that. "Pluto was a planet when I grew up, so how can it not be a planet now?" Easy, a planet is a CATEGORY created by CONVENTION, and conventions change. That's not denying that the physical oblate spheroid doesn't exist or has changed, but the rules of the language game have because 'what is a planet' has gone from everybody gets a vote to the members of the IAU get a vote. (This also highlights the difference between folk categorization and folklore and technical categorization by domain-specific experts and jargon.)